Abstract: Postsingularly finite holomorphic functions are entire functions for which the forward orbit of the set of critical and asymptotic values is finite. Motivated by previous work on approximating entire functions dynamically by polynomials, we ask the following question:

Given a postsingularly finite entire function f, can f be realised as the locally uniform limit of a sequence of postcritically finite polynomials?
In joint work with Nikolai Prochorov and Bernhard Reinke, we answer this question in the affirmative.